# Integral of Composition Functions

1. Oct 23, 2012

### kuskus94

1. The problem statement, all variables and given/known data

http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc6/282312_368248176595083_1229435302_n.jpg [Broken]

2. Relevant equations

To subtitute x into U, but that did not work.

3. The attempt at a solution

I have tried subtituting x into U like this :

http://sphotos-g.ak.fbcdn.net/hphotos-ak-snc7/578486_368249266594974_1874868606_n.jpg [Broken]

The last two lines are my "goofing around" answer. :tongue2:

Last edited by a moderator: May 6, 2017
2. Oct 23, 2012

### clamtrox

If you change variables, you have to change them all! You can't just leave some x's laying around. Now you have x=x(u) and you don't know how this integrates.

There is kind of a standard trick for any integral that looks like this, which is to first complete the square. What you want to do is to write the integrand into a form
$$\frac{dx}{\sqrt{A^2 - (B+Cx)^2}}$$
and then do a trigonometric substitution $B+Cx = A \sin t$